Implementation and validation of the curvilinear coordinate method for the scattering of electromagnetic waves from two-dimensional dielectric random rough surfaces

The curvilinear coordinate method is an exact method based on Maxwell's equations under covariant form written in a nonorthogonal coordinate system. In this paper, the C-method is applied for analysing 2-D dielectric random rough surfaces. For each medium, this method leads to an eigenvalue system. The scattered fields within two media are expanded as linear combinations of eigensolutions satisfying the outgoing wave condition. The boundary conditions allow the scattering amplitudes to be determined. The coherent and incoherent intensities are estimated by averaging the scattering amplitudes over several realizations. The theory is verified by comparison with results obtained by other exact method. A discussion on the C-method and the Sparse-Matrix CAnonical Grid method is proposed in terms of accuracy and computation time.